Over at the Volokh Conspiracy, Bernard Harcourt explains at length why certain conclusions about the larger societal effects of imprisoning people aren't as robust as they should be, since they don't count those in mental institutions in their figurings about the rises and falls in incarcerated Americans.
It's very detailed and worth reading (and link-hopping) in its entirety to understand the full implications of what he's on to here, but here's the heart of it. Criminologists have generally
used the imprisonment rate to measure society's level of incapacitation. But the prison rate alone may not capture what we were trying to measure. The most straightforward interpretation of my findings is that neither the rate of imprisonment alone, nor the rate of mental hospitalization alone are good predictors of serious violent crime over the period 1934-2001. In contrast, the aggregated institutionalization rate (aggregating the mental hospitalization and prison rates) is a strong predictor of homicides. This suggests that there is something going on in the relationship between mental hospitalization and prison — perhaps a form of substitution — that should make us rethink entirely how we measure social control and incapacitation.
But since practically none of our studies on prisons, guns, abortion, education, unemployment, capital punishment, etc., controls for institutionalization writ large, most of what we claim to know about these effects may be on shaky ground.